What RoAS is a 25% ACoS?

The conversion

RoAS = 1 ÷ ACoS, with ACoS as a decimal. ACoS = 1 ÷ RoAS. That is the whole thing. There is no adjustment, no fudge factor and no difference in what is being measured.

Then why do both words exist?

Habit, mostly, and audience. Amazon's console reports ACoS, so marketplace sellers think in it. Meta and Google report RoAS, so performance marketers think in that. When one team runs both, the two numbers end up in the same meeting describing the same thing and confusing everybody.

There is one real difference in feel. ACoS gets worse as it rises and RoAS gets better, so a chart of the two runs in opposite directions and reading the wrong one has cost people budget decisions.

The trap in the conversion

Converting cleanly between the two encourages the assumption that a good number in one is a good number in the other. It is not, because neither is good or bad in isolation. Both are only meaningful against your break-even.

A 25 percent ACoS is excellent on a product with a 45 percent margin and a quiet loss on a product whose real break-even, once returns are counted, sits at 16 percent.